Question

Graph the two equations to solve the system. What is the solution?
3x + 2y = 6 and y = -3/2 x - 1

(1, 1.5)

(2, 0)

no solution

infinitely many solutions

Answer 1

here is the graph from desmos

Answer 2

we can see there is no intersection to the lines --meaning no solutions.

parallel lines have same slope
y=mx+b m is the slope
y= -3/2x - 1 -3/2 is the slope

if we change the standard line form equation Ax+Bx = C into
slope intercept form y=mx+b

3x + 2y = 6
3x-3x+2y = 6-3x
2y = 6-3x

2y/2 = 6-3x/2
y = -3/2 x +3

slope - 3/2

same slope = parallel therfore no solution.